Reflections of a Communication Engineer

R E P O R T F O R A N A L Y T I C A L C H E M I S T S

Reflections of a Communication Engineer by MARCEL J. E. GOLAY The Perkin-Elmer Corp.

Analytical Chemistry generally publishes texts of addresses of recipients of awards granted at ACS meetings in the area of Analytical Chemistry. Included are the Fisher Award in Analytical Chemistry, the Sargent Award in Chemical Instrumentation, and the Labline Award in Chromatography and Electrophoresis.

The editors feel that the award address of Dr. Golay, recipient of the Sargent Award, although not of direct analytical interest, is a thought-provoking philosophical approach which should be of interest to all scientists. The editors are presenting it as this month's Report for Analytical Chemists.

Τ CANNOT TELL A LIE—I am not a chemist. That is why I have

decided to change the subject of my talk. Others will tell you, more competently than I could, about the physical chemistry of chromatography. It is as a communication engineer that I will talk to you. And if the things I say increase in strangeness as I go along, I will ask you to remember two things.

The first is this: Many of the recent advances in science are due to the cross-fertilization of, at first view, separate and distinct fields.

And the second is this: Of all the disciplines guilty of such fruitful incests, communication engineering is the guiltiest of them all, with its inroads in physics and chemistry, in biology, in sociology through automation, in philosophy through information theory. Communication engineering—or should I say communication philosophy— appears as an octopus, with its tentacles stirring thought here, there, and everywhere, an octopus intimately linked to the development of social man, and to the reflections of individual man.

I owe the good fortune of being with you today to the accident of having noted that, in a simplified

form, the chromatographic partition process could be described by the telegrapher's equation. Nothing more would have happened if my friends at Perkin-Elmer had not asked me to stick numbers in the equation—after all, a consultant must earn his keep. This led to the finding that the packed chromatographic column of five years ago had a basic efficiency, as measured by the Performance Index, of around 0.01%. This finding led in turn to the idea of making a column which had the form of the simple model adopted for the theoretical study—namely, an open tube coated with a retentive layer. That is all.

I said I would talk as a communication man about communication philosophy and the strange lands where it may take us. It is not every day that I have the opportunity of talking to a kindly inclined and nearly captive, well guarded audience about my extracurricular thoughts, and I will start with a reminiscence. I will reminisce about a time when I was a little boy, going shopping with my mother, walking alongside, and trying to digest something metaphysical I had read, which I was

probably too young to read. Yet all of a sudden, all my thoughts came into a focus, and I started to speculate: Suppose there had been nothing at all, no time, no space, no matter, no people. But there is something and I am part of this something, playing my role in it. There was rain falling on the pavement on that day and I remember that, too.

Surely the simple thought that there is a universe and that we should not be indifferent to our privilege of playing our part in it has been the underlying incentive to the building and the evolution of our philosophy and cosmology.

The beginnings of our cosmology appear naive in retrospect. Some of you may recall learning in your history class about the early mythological world, flat and carried by a large elephant, with his feet on four turtles swimming in a sea of milk. Little by little these notions became purified. We made a notable step forward when we accepted a universe not centered in our little earth. For a long time the concepts associated with the origin of our universe oscillated between an instinctive belief in a beginning, a creation, and a scientific opinion that we lived in a static universe with time stretching indefinitely backwards and forwards. And then, last century, budding physical chemistry led us to a real difficulty.

I t was in the early part of the last century that Carnot formulated what became accepted as the second law of thermodynamics. As further developed by Helmholtz, this law stated, in effect, that there is a continuous degeneracy, a continuous decay of energy. You can mix hot and cold water, but you cannot unmix them.

When you extend this principle to our whole universe—and it is the virtue of any principle that you can do so with it—you come to the

VOL. 33, NO. 7, JUNE 1961 · 2 3 A

REPORT FOR ANALYTICAL CHEMISTS

Figure 1

Figure 2

Marcel Jules Edouard Golayis one of the rare scientists alive today deserving of the title of natural philosopher. His vigorous mind has an equally tenacious grasp on both the abstract and the concrete. Indeed, he is sometimes accused by friends of failing to differentiate between the two, and those who have driven with him in his sports car are particularly conscious of his tendency to divorce physical problems from their immediate context.

In keeping with this natural bent, Golay's contributions to science are almost equally divided between theoretical concepts and practical applications, and he is inclined to produce ideas first, seek physical means of carrying them out second.

Animated, bon vivant, articulate, restless, often contentious, always eminently practical, Golay values money only for the things it can buy. He can, on occasion, be as sensitive to praise or criticism as any operatic diva, and characteristically views himself with a benign detachment from conventionality. Typical of this habit of thought was his recent Sargent Award Address, announced as "Our Present Understanding of the Gas Chromatographic Process," which actually turned out to be a discussion of cosmology, directly related to gas chromatography only by Go-lay's impartial interest in both.

Golay was born in Neuchâtel, Switzerland, in 1902,

Golay's brilliant static multislit invention is based on Boolean algebra. It permits a spectrometer to have the resolution afforded by a narrow slit but the light gathering power of many slits. This series of figures show schematically how the idea works for a pattern of 16 slits.

Figure 1. A Golay multislit pattern representing the exit slit of a monochromator. White spaces are openings.

Figure 2. This pattern represents the image of the entrance slit of the monochromator. Both patterns are made up of 4 rows of open or closed spaces with widths which are multiples of one of the narrow units.

Figure 3. In the spectrometer, the entrance pattern is

Figure 3

2 4 A · ANALYTICAL CHEMISTRY

Marcel Jules Edouard Golay


obtained his Baccalauréat Scientifique from the Gymnase de Neuchâtel in 1920, and his Licentiate in Electrical Engineering from the Federal Institute of Technology in Zurich in 1924.

A member of the Bell Telephone Laboratories staff from 1924 to 1928, he worked on a number of projects and during that period invented a velocity microphone and an electrostatic method to test the dielectric strength of telephone cables.

In 1928 Golay entered the University of Chicago and received a Ph.D. degree in 1931. His thesis in atomic physics dealt with an experimental elucidation of some energy levels in mercury.

On graduation he joined the Signal Corps Laboratories. One of his more significant assignments during this period was in the area of infrared radiation and resulted in the development of the Golay pneumatic infrared detector, initially conceived as an aircraft detecting device. Later the Golay detector was applied to the infant science of infrared spectroscopy, and even today remains the most sensitive room-temperature detector available.

The Golay detector, in its intricacy and elegance, is characteristic of Golay's inventions. Its effective blackness derives from use, as an infrared receiver, of a film whose electromagnetic impedance matches that of free space. Heat collected by the film is used to

imaged on the exit pattern and light can only come all the way through spaces open in both patterns (the white spaces). If the top two rows are considered as one field and bottom two rows as another field, there are an equal number of openings in each.

Thus subtracting the signal which measures the total radiation coming through the bottom field from that coming through the top field, yields zero. This can be done with differential detectors or differential chopping of the two fields.

Figure 4. In scanning the wavelength, the entrance (gray) pattern progresses over the exit pattern moving to the right. This produces a different distribution of open-

Figure 4

run a heat engine which moves a mirror; mirror motion is detected by optical means. Sensitivity of the heat engine is limited only by Brownian motion; that of the optical detector, by diffraction and granulation of light. Over-all sensitivity of the system is only slightly less than the theoretical limit.

Another Golay invention, so far ahead of its time that it is still not fully exploited, was the multislit infrared spectrometer. Conceived by Golay in 1948, the spectrometer is an almost purely mathematical invention based on binary algebra, whose l's and O's Golay made to represent open or closed spaces in the entrance and exit slits of the spectrometer.

In order to create a functioning spectrometer, Golay initially required a rotating disk with many fine, precise multislit patterns. For its manufacture—in the basement of his home—he invented a method of ultra-precise photoetching of thin metal foils, so successful that it is now used by leading producers of photoetched foil components.

The photographic master required for Golay's disk in turn involved design of a kind of "ruling engine" which, connected by Golay to a novel relay computer to generate l's and O's, makes exactly 214 white or black marks on the photographic master. A subsequent multislit logic developed by Golay eliminated the rotating pattern.

ings but still the same number above and below. This happens for all relationships of the two patterns except one.

Figure 5. This is the magic position. In scanning the space of one unit slit, the top pattern has become completely open and the bottom completely shut. The difference between the two has jumped from zero to a very large value. Thus for one narrow wave length, the difference signal is very large.

Dr. Golay has worked out 15 sets of patterns for this remarkable invention including one having 216 slit spaces per row.

Figure 5

VOL. 33, NO. 7, JUNE 1961 · 2 5 A

In 1955 Golay resigned his position as chief scientist of the Components Division of the Signal Corps Engineering Laboratories to devote a major portion of his time as consultant to the Philco Corp. of Philadelphia in network and information theories, and to The Per-kin-Elmer Corp. of Norwalk, Conn., in infrared and nuclear spin resonance instrumentation, gas chromatography, and pyrometry.

One of the first problems he faced at Perkin-Elmer was that of curing the inhomogeneity of magnetic fields which limited resolution available in nuclear magnetic resonance spectrometry. His proposal to "degauss" the inhomogeneous part of the field with current-carrying coils that generated equal but opposite inhomogeneous fields at first appeared impractical ; when more than three such coils are used, the result is such a morass of interaction that adjustment is virtually impossible. This, however, is not what Golay had in mind. His intent was an orthogonal degaussing with magnetic fields conforming to a set of functions called spherical harmonics, which would be independent of one another in any actual experiment.

Producing these magnetic fields required sheets of varying current density either on a sphere or on two parallel planes. Golay made his earliest planar coils by embroidering with fine electrical wire on a piece of cloth stretched on an embroidery hoop. A method of manufacture more suitable for volume production was later devised using printed circuits. The fields derived from these coils are almost perfectly orthogonal and sets of 13 coil pairs providing 13 independent cancellations of inhomogeneity are now in general use. They are, of.course, called Golay coils.

Golay's involvement in gas chromatography began in 1956 with his paper "Vapor Phase Chromatography and the Telegrapher's Equation," based entirely on mathematical considerations. It was, in fact, not until after the presentation of this paper that Golay first saw a gas chromatograph. Subsequent attempts to fit his theoretical treatments to experimental results proved difficult for conventional packed columns, and with typical insight, Golay turned to the open tubular column now known as the Golay column.

The small-bore, early Golay columns, if they were short, required tiny detector volume and even tinier injection volume. No equipment like this was avail-

Figure 6. With this t iny chromatography unit, which he designed, Golay got the first cathode-ray chromato-grams using an open tubular column


able at that time, so Golay designed it. The essential component was the detector, then conventionally a catharometer with a volume of 1 cubic centimeter which would have hopelessly obscured the recorded peaks. Golay's detector had a volume of 2 cubic millimeters, and provided the first cathode-ray chromato-grams using an open tubular column.

Early Golay columns were capable of superb performance, but were difficult to work with. Many of these problems have been solved and today we have familiar, highly engineered forms of Golay columns with compatible ionization detectors.

In gas chromatography, the Performance Index proposed by Golay is gaining recognition as the true measure of the efficacy of a gas chromatographic column. Golay columns are acknowledged as the greatest single technological advance since the invention of the gas chromatographic column in 1940.

Among Golay's many other accomplishments and inventions were the development of equivalent circuit constants for a Rochelle salt "bimorph," invention of a double-grid hot-wire sound ranging microphone, a complete theoretical solution to the problem of devising a dispersionless delay line, a practical design for what is now called the Golay delay line, and important basic concepts applicable to communication theory.

In 1950 Golay received the Harry Diamond Award of the Institute of Radio Engineers for his scientific work as a civil servant, and more specifically for his work in far-infrared instrumentation and detection.

In 1961 his contributions to the general field of instrumentation were recognized by the American Chemical Society Award in Chemical Instrumentation, sponsored by Ε. Η. Sargent and Co., presented to him at the 139th Meeting of the ACS in St. Louis in March.

Golay holds 16 United States patents, not an enormous number by the standards of a Steinmetz or a Kettering, but distinguished by the extremely wide variety of their fields and approaches. They include one on infrared modulation systems, a mathematical invention; the dispersionless delay line, another mathematical invention; a physical invention, the infrared detector, characteristically small, complex and intricate; and current paths on spheres to generate spherical harmonics, a mathematical abstraction.

As Golay has been at work for a good many years now, a few of his inventions have lost a measure of their practical importance through age. Yet all remain intellectually admirable, and quite characteristic of this dynamic, creative scientist.

Prepared by John G. Atwood and H. Newell Claudy The Perkin-Elmer Corp.

VOL. 33, NO. 7, JUNE 1961 • 2 7 A

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metaphysical conclusion that this irreversibility of nature's processes demands that there be a definite beginning, a creation. But the semireligious concept of a creation, with the corollary concept of a Creator, was scientifically inadmissible, so it was thought, and matters stayed in that impasse through three generations of scientists. In order to get out of this difficulty, as able a philosopher as Poincare made intellectual somersaults worthy of a devil caught in the holy fonts. He surmised, for instance, that if time marched forward in one part of the universe, this was made up by time going backward in some other regions, which is, of course, inadmissible. The clock cannot run backward.

STATIC UNIVERSE CONCEPT IS UNTENABLE

Things were in this impasse when two additional discoveries, taken together, made the concept of a static, uncreated universe completely untenable. The first was the discovery of radioactivity. Many natural radioactive isotopes such as thorium, uranium, and potassium have a very low rate of decay, and the fraction remaining today, establishes a rough epoch for their creation, of the order of several billion years ago.

The second discovery was made by the astronomer Hubble in an entirely different domain. Hubble

observed that many large galaxies are receding from us at a high speed. Galaxies are assemblies of from a billion to a quadrillion stars, and as they recede from us their characteristic color is shifted towards the red. Hubble observed that the farther the galaxies, the greater the red shift. But we are not in the center of the universe. The universe has no center in the sense that an orange has a center. Thus every galaxy must be receding from every other. This can only mean that we have a general explosion, and Hubble calculated that galaxies receded from each other as if this general explosion started at roughly the same epoch already determined by a study of the rate of decay of our radioactive minerals.

I t was a Belgian cleric, the Abbé Lemaitre, who cut the Gordian knot by saying: "Let us postulate that the whole universe started several billion years ago with a single enormous atom." And it turned out that his daring hypothesis led to fewer difficulties than any other. This is the decisive test of any physical theory. The postulate of Lemaitre is generally accepted today, and you will find in the scientific literature quite serious speculation as to the state of the universe two minutes after its creation, for instance.

You may well ask: But what was there before and why did it all

Figure 7. Successive stages of a 3-D spherical universe expanding in a 4-D cosmos shown by section with plane passing through embryonic universe

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start? And of course, the question must remain unanswered.

You may well ask also: Did it start with a pin-point of matter of no size and infinite density? This is an interesting question to think about, for the following reason. When we permit two masses to come together by gravitational attraction, like a mass of water falling towards the earth center through a hydroelectric plant, we derive useful energy at the expense of the negative gravitational potential energy of these two masses. And when we calculate that total negative gravitational energy for the entire universe, using available astronomical data, we find that it is of the order of magnitude of the total positive energy in the form of masses, radiation, kinetic energy, and so forth. So we are led to ask: Could it be that the total energy of the universe is actually zero, that the positive energy we have in the form of mass and radiation is merely the result of a trade for negative gravitational energy? Then, if this is so, perhaps the Creator did not require the enormous mass of all the stars that we see, but required merely the intelligence to trigger the process, after which it kept going. We shall come back to this, but let us, for the time being, remember that some ten billion years ago a quite extraordinary event took place, beyond which the veil of history is forever closed to us.

FIRST PROTOZOIC LIFE Now let us look at another his

torical puzzle, of a completely different order. Some two billion years ago, when our universe was already several billion years old, another extraordinary event took place on this earth. It was nothing as spectacular and grandiose as the creation of our macrocosm. It was microscopic in nature, but may turn out to be the most significant thing in the history, not of just our little earth, but of our entire universe. I refer, of course, to the appearance of the first protozoic life. After its creation, life evolved, and culminated in the appearance of man. Last century this process of evolution, especially in its last stages,

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was a subject of debate and controversy. Much ado was made about missing links, but today we think we understand better this evolution process, and why few ancestral forms, not just of man, but of most living creatures, are ever found. What we do not understand is the very beginning of the process, what produced this first molecule? We may be tempted to be superficial and shrug off the question by saying that the first living molecule was produced by chance, but let us give this problem a second look, in the light of information theory.

NEW DISCIPLINE-INFORMATION THEORY

Information theory is a recent addition to our family of disciplines and it deals with a subject which is closely related to the second law of thermodynamics, the very law which stated that the passage of time is marked by a decay of energy, and hence that there must have been a beginning to our universe. In many respects information theory constitutes that chapter of communication theory which has had, and will continue to have, an impact on metaphysics and philosophy.

The beginnings of information theory are curious. Nearly a century ago Maxwell expressed his impatience with the second law of thermodynamics by inventing a little demon, Maxwell's demon, which was to haunt two generations of scientists. As you know, Maxwell's demon is perched by a trapdoor in a wall separating two identical gas masses, and every time a molecule comes from the first gas mass in the direction of the trapdoor he opens it for an instant and lets that molecule pass through to the second gas mass. After a while you have more molecules and more gas pressure in the second gas mass than in the first, and that extra gas mass can expand into the first and produce useful work, while cooling. This constitutes a violation of the second law because useful work has been obtained from the heat of two gas masses originally in temperature and pressure equilibrium. A good paradox deserves a good an-


REPORT

swer, and a clever demon deserves a clever exorcism, and it was not until 1929 that this was done by the physicist Szilard, who said that Maxwell's demon cannot operate, because he does not have the information as to when to open his trapdoor.

For some 15 years Szilard's article remained unappreciated by almost everyone, including Szilard himself: His original manuscript had been noticed on his desk by friends, who persuaded him to let them mail it to their scientific journal; otherwise it might have remained unpublished. But shortly after the last war, certain statistical aspects of the theory of communication became of interest simultaneously to several researchers. In 1948 Shannon published his classic article, which became the foundation of information theory. In this article he noted the similarity between the entropy of the ther-modynamicist and the negentropy of information. If you will pardon a personal reference, I heaped the last indignity on the poor demon when I showed that even with the most efficient transmission system, the energy required to communicate to the demon the information he needs would at least equal the useful energy he could retrie\re by operating his trapdoor. So, even if the information the demon needed were available at no cost, it could not be communicated to him, without destroying his raison d'être.

I am talking at length about information theory because of the dualism between the second law and information theory on the one hand and the dualism between the creation of the universe and the creation of life on the other hand. It is information theory, and the new scientific attitude produced by information theory, which has revealed some interesting aspects of living molecules and living cells.

Information theory has taught us how to deal quantitatively with structure, with pattern, with what the Germans call Gestalt. Even beauty and esthetics are tentatively admitted to the community of scientific concepts by information theory.

We can place within the scope of

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information theory the following problem, which was examined by the mathematician Von Neumann. Suppose we wanted to build a machine capable of reaching into bins for all of its parts, and capable of assembling from these parts a second machine, just like itself. What is the minimum amount of structure or information which should be built into the first machine? The answer came out to be of the order

of 1500 bits—1500 choices between alternatives which the machine should be able to decide. This answer is very suggestive, because 1500 bits happens to be also the order of magnitude of the amount of structure contained in the simplest large protein molecule which, immersed in a bath of nutrients, can induce the assembly of these nutrients into another large protein molecule like itself, and then sepa-

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rate itself from it. That is what the process called life consists of, and unless and until we discover a new process in which simpler molecules have semilife properties, the inquiry into the birth of life can be reduced to an inquiry into the possibility or probability of the spontaneous assembly of such a molecule, out of a bath of its essential constituents. And this is exactly where we run into an interesting difficulty.

SPONTANEOUS CREATION OF LIFE?

By making the most favorable assumptions as to the conditions in which this spontaneous creation of life could have occurred on this earth, we do not come anywhere near the spontaneous assembly of 1500 bits; we can account for perhaps one tenth that number. Do not shrug this off as being only one order of magnitude off. This involves a factor of 10 in the exponent, and there is a vast difference between the probability of 1 part in 21B0 and 1 part in 2150°. Then you might say: But it could have happened in many places in our universe, and if it had not happened here, we would not be here to talk about it.

Very well, multiply 2150 by the number of stars—that is, by the number of potential solar systems, in the universe—and you obtain 2220, still short of the mark. And yet, life did begin, and looking back in time, we see two mysteries, or at least two highly unlikely events. The first, the creation of the universe, of space, of time, of matter. The second, the creation of life, from which we evolved as a matter of course almost, with such unlikely beings as physical chemists in our midst, producing in the laboratory improbable assemblages such as a liter of liquid helium, or saying such unlikely things as what I am now saying to equally unlikely assemblies of molecules as my listeners. We may even have some day an,unlikely biochemist who will assemble, radical by radical, an unlikely large molecule which can reproduce itself. But this would not resolve the historical mystery of the creation of the first living molecule.

TWO BIG QUESTIONS OF THE FUTURE

All I have said so far has been to prepare the ground for two big questions, dealing with what could be called the two basic mysteries of the future.

The first big question is philosophical, and can be stated fairly simply. With his intelligence, with his ability to make experiments and to process information, does man have the potentiality of ever acquiring full information about the basic laws of nature? I am sure all of us have asked ourselves this, or a similar question. Some of us believe that the final truth will always escape us, even though every discovery, every mathematical theorem brings us closer to it. Others of us believe that when we run into integral numbers, such as the number of protons and neutrons in a nucleus, we are approaching the ultimate basic knowledge. Tied to this first big question, there are other tempting questions. For instance, we have an information theory which has established a measure for the amount of information we can communicate to each other. Shall we, some day, have a measure of intelligence, or will intelligence always transcend a definition of itself? And even if we succeed in defining and measuring intelligence, shall we some day prove mathematically the impossibility of intelligence reaching the ultimate truth, just as the mathematician Godel has proved the existence of un-demonstrable theorems? Shall we perhaps come to the paradoxical proposition that a supreme intelligence should disprove the possibility of its very existence?

I do not want to linger on this speculation, no matter how fascinating it may be. I want to come to the second big question.

While we do not know whether or not we shall be able some day to unravel the last shred of mystery surrounding the truth of the universe we live in, we do know, from the second law of thermodynamics, that the clock cannot run backward, and that our universe is condemned to eventual total decay, to end, as T. S. Eliot has put it, not with a bang but

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with a whimper. Shall we sit helplessly by watching t ha t process, until even the modest wants of life as we know it can be no longer supplied?

Alternatively, is there a possibility tha t human intelligence will have the capability of doing something radical about the situation?

At first glance, the answer would seem to be "no" ; the second law drives the universe inexorably to

eventual decay, and regeneration is ruled out. I t is a t this point tha t I would interject a very timid "but." Remember tha t the world may well have been triggered into existence by a highly intelligent act producing a highly unlikely event—remember t h a t the total energy of the universe may be very small, maybe even zero, the creation of mass having proceeded a t the expense of negative gravitational en-

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ergy. Could it become man's role to be the author of a similar highly intelligent act, before the clock of his universe becomes unwound?

MATTER-NEGATIVE GRAVITATIONAL ENERGY EXCHANGE

I admit this sounds fantastic, because we have today no inkling of the mechanism involved in any trade of positive energy in the form of matter for negative gravitational energy. I must ask you to remember tha t , so far, physicists have not succeeded in performing a single experiment which connects gravitational phenomena with electrical phenomena, because electrical forces between elementary particles are some 40 orders of magnitude larger than gravitational forces. We are, therefore, at the point where metaphysical arguments must take over from physical arguments. T h a t is, we may assume yet undiscovered mechanisms, while being careful not to violate already established physical principles.

I have pointed out before that we, men, these highly unlikely but intelligent creatures, have pr luced such unlikely things as a liter of liquid helium, something never produced spontaneously before anywhere in our universe.

Suppose now tha t our colleagues, the nuclear chemists, were to succeed in engineering a relatively heavy neutral particle, of extremely small volume, and of extremely low probability of spontaneous generation, just like the liter of liquid helium. Keep on supposing tha t this new particle has sufficient interaction with ordinary mat ter as we know it, and once produced in some supercosmotron, trickles gently toward the center of the earth, where it coalesces with others like itself into a very small mass of extraordinarily high density. The manufacture of these particles continues, and in a little while this small mass has the size of an electron. Later on, after many more particles have been produced and assembled, this small mass acquires the size of a molecule. But this is an important project, and eventually a few millionths of our earth mass have been thus transformed and poured in the ground, to re-


assemble in the earth's center into a tiny sphere, one wave length of light in diameter. Some very interesting things could begin to happen by then. Remember that space is curved by mass. Oh, very little. But on the mass surface, this effect is in inverse proportion to the radius of that mass. And I have postulated a very, very small size of extraordinarily high density. By the time our small but enormously heavy mass has reached a wavelength of light in diameter, it has almost wrapped its own space around itself, and has become very close to what I would call a gravitational "crit." I believe we are about to have a gravitational explosion.

Before it is too late, let us review our calculations. Take a certain mass and distribute it in the physical space of a universe which has the shape of a three-dimensional spherical bubble within a four-dimensional cosmos. Then stipulate that the total mass-energy of the system, which is equal to the initial mass-energy plus the rela-tivistic increase due to the speed of expansion, is also equal to its total negative gravitational energy. This is the same as stipulating that the total energy of the system is zero, and no simpler stipulation can be made. Write this down as an equation, for which we need only the initial mass, the gravitational constant, and the speed of light. Solve this equation and examine the solution you obtain (1.). This solution represents an explosion which proceeds with nearly the speed of light, with a continuously increasing mass but also a continuously decreasing density. And if you substitute the age of the universe today for the time appearing explicitly in this solution you obtain a density of the order of 10"30 gram per cc. This is the density of our present universe, within the margin of observational error. And if you like, make the initial mass from which you started, zero, and the solution is hardly affected. No known physical law has been violated in this calculation, but a yet unknown mechanism has been postulated for the trade of positive mass-energy for negative gravitational energy.

This is an intriguing result, which

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leads to the following picture. Imagine a two-dimensional plane

intersecting our three-dimensional universe within the four-dimensional cosmos I have assumed. This is similar to a plane intersecting a two-dimensional sphere within a three-dimensional space, and if this plane is the blackboard, we have a circle which expands. But we have chosen a plane which passes through the center of the earth, and here there is an increased curvature as we approach our tiny, enormously heavy mass. The experiment continues, the mass increases in weight, the curvature of space increases on both sides, and a critical point is reached when it wraps its own space around itself, shearing itself from its mother-universe, and beginning to expand on its own.

This picture may induce some final soul-searching questions, before fabricating the additional billion tons or so of our heavy particles, which will produce a gravitational crit in the center of our beloved planet.

DESTRUCTION OF UNIVERSE UNLIKELY

Will this supreme experiment destroy our old universe while creating a new one? Probably not. Any annihilation of the universe would require its collapse, and anything resembling a return to the beginning implies an unlikely turnabout of the clock.

Will it create a local disturbance, of the order of a supernova, hardly felt in other solar systems of our galaxy, and barely observed from neighboring galaxies? Or will it produce only a cosmic seed which, wrapping its own space around itself, will make a clean break with the old universe, becoming a new and full-fledged three-dimensional universe of its own, within the four-dimensional cosmos containing all there is? A completely separate new universe, having no physical connection with the old, and producing its own stars and its own living and thinking creatures, who shall know of us no more than we shall know of them, like these ephemeral insects who never coexist

with their parents and their offsprings.

At this point I would like to ask you not to take too literally some of the things I am saying. I admit their fantasy makes them sound like science fiction literature. I could say nothing about the mechanism involved. In the absence of any physical experiment connecting electrical phenomena with gravitational phenomena, I could only assume the existence of such a mechanism based on the probably non-linear character of the field equations which would eventually connect electrical and gravitational phenomena, while being careful not to violate known laws. I have glossed over such serious difficulties as those which arise if we have the possibility of multiple creation, with several junior universes blow-, ing up like smaller soap bubbles within the mother bubble, first interacting and then beginning to interfere with each other. I have not discussed what meaning can be a t tached to a world mass which consists almost entirely of the incremental relativistic mass of a van-ishingly small initial mass. I have no good answer for several sound logical and even embarassing questions about these and other points. I can only plead for a measure of license, when speculating about a nonrepugnant al ternative to a philosophically repugnant once and for all universe, doomed to eventual decay, or to a physically untenable infinite universe stretching indefinitely backward and forward in time.

I said I would not ta lk about chromatography, and I th ink I have succeeded in that . I hope to have succeeded also in giving you an idea of the strange lands to which we may be led by communication philosophy, and by speculation about the clock-rewinding task which may challenge the intelligence of man.

(1) Golay, Marcel J. E., "On a Connection Between Mach's Principle and the Principle of Relativity." The Observatory 79, No. 912, pp. 189-90.

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